Some who are eligible to vote may not be eligible to drive.
I think that a national ID card is not a bad idea. Some raise concerns about the potential abuse of such a document, but the fact is that there are no weaknesses in a national ID system that do not currently exist in the driver's license databases.
Each state could still be responsible for issuing an ID, but it would be on a federal standard form. The ID should be a multi-function document. Not only should it contain information to identify the owner, but it should also serve as a driver's license, fishing or hunting license, boating etc. Plus it will serve as the bearer's voter identification.
That way those who do not drive will have the same method of identification as everyone. Entering the information into the state's database will make voter fraud more difficult.
This would also get around the issue of absentee ballots. The absentee voter would simply enter his license number on the form.